In order to characterize the empirical K-values and determine how far off the analytical model was, a testing and validation setup is described in this section.

Dynamometer

Pictured: Power Test Dynamometer.

When driven, a BLDC motor produces a three-phase AC voltage output. This voltage and resultant motor speed depends on the KV rating motor, which can be extracted when both are measured.

\[KV = RPM/V\]

Additionally, current is generated as a function of voltage generated and total impedance Z:

\[I = V/Z\]

Where Z is the sum of the motor internal phase resistance $R_{phase}$, external load resistance $R_{load}$, and inductive reactance (AC opposition) $X_L$:

\[Z = R_{phase} + R_{load} + X_L\]

Inductive reactance is present when voltage and current are constantly changing, dependent on frequency:

\[X_L = 2\pi * f * L\]

However, reactance is dominant in higher RPMs (6000RPM+). For low RPMs, the impedance characteristics can be calculated without reactance:

   Low RPM (<2000) : $Z \approx R_{phase} + R_{load}$

   Medium RPM (2000-6000) : Z = $\sqrt{(R_{phase} + R_{load})^2 + X_L^2}$

   High RPM (>6000) : $Z \approx X_L \approx 2\pi * f * L$

This current is related to braking torque, calculated as follows:

\[T_{brake} = K_t * I\]